A Numerical and Experimental Analysis of a Chain of Flexible Bodies

1994 ◽  
Vol 116 (1) ◽  
pp. 73-80 ◽  
Author(s):  
Marco Giovagnoni
Keyword(s):  
Virtual Work ◽  
Equations Of Motion ◽  
Numerical Data ◽  
Small Displacement ◽  
Flexible Bodies ◽  
Rigid Link ◽  
Body Dynamics ◽  
A Chain ◽  
Multi Body ◽  
Kinematic Solution

A flexible multi-body dynamics approach is described. It uses an equivalent rigid link system from which are measured small displacements. The equations of motion are obtained by direct application of the principle of virtual work. Some terms in the virtual and real components have been neglected by virtue of the small displacement assumption. The use of sensitivity coefficients allows one to obtain a formulation which can be easily interfaced with any kinematic solution algorithm. It also enables one to check the correctness of the chosen equivalent rigid link system. The theory is then employed to reproduce numerically the experimental recordings obtained from a flexible linkage. Agreement between experimental and numerical data is good.

Modeling and simulation of planar flexible link manipulators with rigid tip connections to revolute joints

Robotica ◽  
2004 ◽  
Vol 22 (3) ◽  
pp. 285-300 ◽  
Author(s):  
S. M. Megahed ◽  
K. T. Hamza
Keyword(s):  
Mass Matrix ◽  
Equations Of Motion ◽  
Flexible Link ◽  
Link Length ◽  
Finite Segment ◽  
Revolute Joints ◽  
Body Dynamics ◽  
Lumped Masses ◽  
Multi Body ◽  
Rigid Zones

This paper presents the basis of a mathematical model for simulation of planar flexible-link manipulators, taking into consideration the effect of higher stiffness zones at the link tips. The proposed formulation is a variation of the finite segment multi-body dynamics approach. The formulation employs a consistent mass matrix in order to provide better approximation than the traditional lumped masses often encountered in the finite segment approach. The formulation is implemented into a computational code and tested through three examples; cantilever beam, rotating beam and three-link manipulator. In these examples, the length of the rigid tips at both sides of each link ranges from 0% to 6.25% of the whole link length. The zones of higher stiffness at the link tips are treated as short rigid zones. The effect of the rigid zones is averaged along with some portions of the flexible links, thereby allowing further simplification of the dynamic equations of motion. The simulation results demonstrate the effectiveness of the proposed modeling technique and show the importance of not ignoring the effect of the rigid tips.

A Moving Frame Method for Multi-Body Dynamics

2013 ◽  
Author(s):  
H. Murakami
Keyword(s):  
Equations Of Motion ◽  
Rigid Bodies ◽  
Explicit Representation ◽  
Moving Frame ◽  
Moving Frames ◽  
Body Dynamics ◽  
Moving Frame Method ◽  
Frame Method ◽  
Multi Body ◽  
Kinematics And Kinetics

Élie Cartan’s moving frame method, developed in differential geometry, has been applied to multi-body dynamics to derive equations of motion. The explicit representation of a body-attached orthonormal coordinate basis and its origin, referred to as a moving frame, enables the usage of the special orthogonal group, SO(3), and the special Euclidean group, SE(3), to describe kinematics and kinetics of interconnected bodies by joints and force elements. The moving frame representation using Theodore Frankel’s compact notation is adopted to alleviate theoretical complexities of the Lie group theory to which SO(3) and SE(3) belong. For the variational formulation, the restricted variation of angular velocity is derived for the moving frame method. Starting from two connected rigid bodies, it will be demonstrated that the explicit representation of moving frames renders straight-forward symbolic computations of three-dimensional kinematics and kinetics. This simplicity eliminates errors in computing analytical expressions for kinematic and kinetic variables and streamlines the coding effort for numerical solution. For controller design, if the degrees-of-freedom is small, the moving frame method allows a straight-forward derivation of equations of motion in analytical form.

Explicit equations of motion for constrained mechanical systems with singular mass matrices and applications to multi-body dynamics

2006 ◽  
Vol 462 (2071) ◽  
pp. 2097-2117 ◽  
Author(s):  
Firdaus E Udwadia ◽  
Phailaung Phohomsiri
Keyword(s):  
Explicit Form ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Constrained Motion ◽  
Holonomic Constraints ◽  
Constrained Mechanical Systems ◽  
Mass Matrices ◽  
Body Dynamics ◽  
Multi Body ◽  
Explicit Equations Of Motion

We present the new, general, explicit form of the equations of motion for constrained mechanical systems applicable to systems with singular mass matrices. The systems may have holonomic and/or non-holonomic constraints, which may or may not satisfy D'Alembert's principle at each instant of time. The equation provides new insights into the behaviour of constrained motion and opens up new ways of modelling complex multi-body systems. Examples are provided and applications of the equation to such systems are illustrated.

Modeling and Simulation of Motorcycle Ride Comfort Based on Bump Road

2010 ◽  
Vol 139-141 ◽  
pp. 2643-2647 ◽  
Author(s):  
Dong Mei Yuan ◽  
Xiao Mei Zheng ◽  
Ying Yang
Keyword(s):  
Degrees Of Freedom ◽  
Ride Comfort ◽  
Lagrange Equation ◽  
Equations Of Motion ◽  
Vertical Displacement ◽  
Dynamics Model ◽  
Body Dynamics ◽  
Space Formulation ◽  
Simulation Results ◽  
Multi Body

Through analyzing the motion when motorcycle runs on the bump road, the 5-DOF multi-body dynamics model of motorcycle is developed, the degrees of freedom include vertical displacement of sprung mass, rotation of sprung mass, vertical displacement of driver, and vertical displacement of front and rear suspension under sprung mass. According to Lagrange Equation, the differential equations of motion and state-space formulation are derived. Then bump road is simulated by triangle bump, and input displacement is programmed by MATLAB. With the input of bump road, motorcycle ride comfort is simulated, and the simulation results are verified by experiment results combined with two channels tire-coupling road simulator. It indicates that the simulation results and experiment results match well; the 5-DOF model has guidance for development of motorcycle ride comfort.

scholarly journals Human Joint Simulation Using LifeMOD Co-Simulation

2008 ◽  
Vol 2 (2) ◽  
Author(s):  
Eric Fahlgren ◽  
Mark Carlson ◽  
Andrew S. Elliott
Keyword(s):  
Chromium Steel ◽  
Large Displacement ◽  
Small Displacement ◽  
Cobalt Chromium ◽  
Artificial Joints ◽  
Walking Gait ◽  
Body Dynamics ◽  
Elastic Responses ◽  
Multi Body ◽  
Ultra High Molecular Weight

Advanced design of human artificial joints requires an in-depth understanding of the dynamic interaction between the very stiff bone replacement material and the softer viscoelastic cartilage replacement material. It must take into account both the large displacement gross motions as well as the small displacement elastic responses. A co-simulation methodology has been developed in BRG LifeMOD, connecting Adams∕Solver, a large displacement multi-body dynamics code, to Marc, a nonlinear finite element code. This efficient co-simulation approach allows for each code to handle that portion of the system for which it is most capable, while adding the potential to work across multiple CPUs and operating systems as desired. The method was applied using LifeMOD∕KneeSIM to simulate an artificial knee joint, containing cobalt chromium steel and ultra-high molecular weight polyethylene contact elements, undergoing a normal walking gait to predict kinematics, forces and the resulting wear patterns.

Analysis of the dynamic contact between rotating spur gears by finite element and multi-body dynamics techniques

2001 ◽  
Vol 215 (4) ◽  
pp. 423-435 ◽  
Author(s):  
K Lee
Keyword(s):  
Finite Element ◽  
Contact Point ◽  
Equations Of Motion ◽  
Mass Effect ◽  
Dynamic Contact ◽  
Spur Gears ◽  
Gear Teeth ◽  
Body Dynamics ◽  
Tooth Surfaces ◽  
Multi Body

A numerical method is presented for the dynamic contact analysis of spur gears rotating with very high angular speeds. For each gear an elastic tooth of distributed mass is connected to a rigid disc with kinematic constraints, and finite element formulations are used for the equations of motion of the teeth. The velocity and acceleration as well as the position of the contact point sliding on the mating gear teeth are precisely computed by simultaneously using the motions of a pair of rotating tooth surfaces. The equations of motion subjected to the kinematic constraint and contact condition are solved by enforcing the velocity and acceleration constraints as well as the displacement constraint. In the numerical simulation the importance of the mass effect of gear teeth is demonstrated, and it is shown that the solution is obtained even if gears repeat contact and separation.

The Use of Zero-Mass Particles in Analytical and Multi-body Dynamics: sphere rolling on an arbitrary surface

2021 ◽  
pp. 1-24
Author(s):  
Firdaus Udwadia ◽  
Nami Mogharabin
Keyword(s):  
Equations Of Motion ◽  
Classical Problem ◽  
Analytical Dynamics ◽  
Homogeneous Sphere ◽  
Constrained Mechanical Systems ◽  
Zero Mass ◽  
Significant Difference ◽  
Mass Matrices ◽  
Body Dynamics ◽  
Multi Body

Abstract Zero-mass particles are, as a rule, never used in analytical dynamics, because they lead to singular mass matrices. However, recent advances in the development of the explicit equations of motion of constrained mechanical systems with singular mass matrices permit their use under certain circumstances. This paper shows that the use of such particles can be very efficacious in some problems in analytical dynamics that have resisted easy, general formulations, and in obtaining the equations of motion for complex multi-body systems. We explore the ease and simplicity that suitably used zero-mass particles can provide in formulating and simulating the equations of motion of a rigid, non-homogeneous sphere rolling under gravity, without slipping, on an arbitrarily prescribed surface. Computational results comparing the significant difference in the motion of a homogeneous sphere and a non-homogeneous sphere rolling down an asymmetric arbitrarily prescribed surface are obtained, along with measures of the accuracy of the computations. While the paper shows the usefulness of zero-mass particles applied to the classical problem of a rolling sphere, the development given is described in a general enough manner to be applicable to numerous other problems in analytical and multi-body dynamics that may have much greater complexity.

A Comprehensive Inverse Dynamics Problem of a Stewart Platform by Means of Lagrangian Formulation

2017 ◽  
Author(s):  
Naser Mostashiri ◽  
Alireza Akbarzadeh ◽  
Jaspreet Dhupia ◽  
Alexander Verl ◽  
Weiliang Xu
Keyword(s):  
Inverse Dynamics ◽  
Virtual Work ◽  
Stewart Platform ◽  
Joint Torques ◽  
Body Dynamics ◽  
Inverse Kinematics Problem ◽  
Simplifying Assumptions ◽  
Inverse Dynamics Problem ◽  
Multi Body ◽  
Lagrange’S Method

In this paper, using the Lagrange’s method a comprehensive inverse dynamics problem of a 6-3 UPS Stewart platform is investigated. First, the inverse kinematics problem is solved and the Jacobian matrix is derived. Next, the full inverse dynamics problem of the robot, taking into account the mass of links and inertia, is investigated and its governing equations are derived. The correctness of the dynamics equations are verified in two ways, first, using the results of the virtual work method and second using the results of a commercial multi-body dynamics software. Because the dynamic calculation is time consuming, two simplifying assumptions are considered. First, the link is assumed to have a zero mass and next it is assumed as a point mass. Studying the former assumption is rather straightforward. However, more complex equations are needed and derived in the present paper for the latter assumption. Required actuator forces for the two assumptions are compared with the case where the mass and link inertial is fully considered. It is shown that the first simplifying assumption significantly affects the accuracy of the required joint torques.

Delta Robot Design

2013 ◽  
Vol 198 ◽  
pp. 9-14 ◽  
Author(s):  
Lukas Březina ◽  
Michal Holub ◽  
Ladislav Cintula ◽  
Jiri Kovar
Keyword(s):  
Flexible Bodies ◽  
University Of Technology ◽  
Body Dynamics ◽  
Pick And Place ◽  
Successful Design ◽  
Dynamics Modelling ◽  
Parallel Kinematic ◽  
Delta Robot ◽  
Multi Body ◽  
The Given

The article proposes an approach to the development of a Delta robot which is the most frequently used robot with a parallel kinematic structure for industrial fast pick and place applications. The approach is model based and it summarizes important steps for the successful design of a Delta robot for the given application including description of the kinematics, multi-body dynamics modelling and flexible bodies notes. This is demonstrated on the particular Delta robot developed at Brno University of Technology (BUT).

An efficient hybrid method for dynamic interaction of train–track–bridge coupled system

2020 ◽  
Vol 47 (9) ◽  
pp. 1084-1093 ◽  
Author(s):  
Zhihui Zhu ◽  
Lei Zhang ◽  
Wei Gong ◽  
Lidong Wang ◽  
Yu Bai ◽  
...  
Keyword(s):  
Hybrid Method ◽  
Equations Of Motion ◽  
Coupled System ◽  
Superposition Method ◽  
Train Track ◽  
Mode Superposition Method ◽  
Body Dynamics ◽  
Direct Stiffness ◽  
Track Bridge ◽  
Multi Body

An efficient hybrid method (HM) is proposed by combining the direct stiffness method (DSM) and the mode superposition method (MSM) for analyzing the train–track–bridge coupled system (TTBS). The train and the track are modeled by applying the multi-body dynamics and the DSM, respectively. The bridge is modeled by applying the MSM that is efficient in capturing the dynamic behavior with a small number of modes. The train–track subsystem and the bridge subsystem are coupled by the interaction forces between them. The computational efficiency is significantly improved because of the considerably reduced number of equations of motion of the TTBS. Numerical simulations of a train traversing an arch railway bridge are performed and the results are compared with the field test data and the data from other methods, demonstrating the efficiency and accuracy of the proposed method.

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